Article Contents
Article Contents

# On the convergence of solutions of the Leray-$\alpha$ model to the trajectory attractor of the 3D Navier-Stokes system

• We study the relations between the global dynamics of the 3D Leray-$\alpha$ model and the 3D Navier-Stokes system. We prove that time shifts of bounded sets of solutions of the Leray-$\alpha$ model converges to the trajectory attractor of the 3D Navier-Stokes system as time tends to infinity and $\alpha$ approaches zero. In particular, we show that the trajectory attractor of the Leray-$\alpha$ model converges to the trajectory attractor of the 3D Navier-Stokes system when $\alpha \rightarrow 0\+.$
Mathematics Subject Classification: Primary: 35Q30, 37L30; Secondary: 76D03, 76F20, 76F55, 76F65.

 Citation: